Question

Is it positive, zero, or negative?​

Answer 1

Discriminant is positive.

Explanation:

From the given graph,

Vertex of the parabola = (-3, -2)

y - intercept of the parabola = (0, 1)

Vertex form of a parabola opening upwards is,

y = a(x- h)² + k

Here (h, k) is the vertex.

By substituting the values of the vertex in this equation.

y = a(x + 2)² - 3

Since this parabola passes through (0, 1)

1 = a(0 + 2)² - 3

a =
`((1+3))/(4)`

a = 1

So the equation of the parabola will be

y = (x + 2)² - 3

y = x² + 4x + 4 - 3

y = x² + 4x + 1

Here a = 1, b = 4 and c = 1 (comparing with standard quadratic equation y = ax² + bx + c)

Discriminant of a quadratic equation is represented by,

(b² - 4ac)

Therefore, the value of discriminant = (4)² - 4(1)(1)

= 16 - 4

= 12

Therefore, discriminant of the given graph is positive.